Ferroelectric crystals Curie temperature

Figure 3.8 Anomalous temperature dependence of relative dielectric constant of ferroelectric crystals at the transition temperature (Curie point).

The ferroelectricity usually disappears above a certain transition temperature (often called a Curie temperature) above which the crystal is said to be paraelectric this is because thermal motion has destroyed the ferroelectric order. Occasionally the crystal melts or decomposes before the paraelectric state is reached. There are thus some analogies to ferromagnetic and paramagnetic compounds though it should be noted that there is no iron in ferroelectric compounds. Some typical examples, together with their transition temperatures and spontaneous permanent electric polarization P, are given in the Table. 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

In particular cases, oxyfluoride compounds with island-type crystal structures, such as K3NbOF6, K3TaOF6, K3Nb02F4 and K3Ta02F4, display ferroelectric-ferroelastic properties, with Curie temperatures of 283, 310, 420, 465°K, respectively [150, 191]. 

Ferroelectricity has also been found in certain copolymer compositions of VF2 with trifluoroethylene, F3E, [6-11] and tetrafluoroethylene, F4E, [12-15] and in nylon 11 [16]. Specifically, copolymers of vinylidene fluoride and trifluoroethylene (VF2/F3E) are materials of great interest because of their outstanding ferroelectricity [9,17-18], together with a parallel strong piezo- [7] and pyroelectricity [19]. These copolymers exhibit, in addition, an important aspect of ferroelectricity that so far has not been demonstrated in PVF2 the existence of a Curie temperature at which the crystals undergo reversibly a ferroelectric to a paraelectric phase transition in a wide range of compositions [9, 17-18],... 

Finally, ferroelectricity is manifest in asymmetrical crystals producing domains of spontaneous polarization whose polar axis direction can be reversed in an electric field directed opposite the total dipole moment of the lattice. The two (or more) directions can coexist in a crystal as domain structures comprising millions of unit cells which contain the same electric orientation. The symmetry elements are temperature sensitive in ferroelectric materials [27]. At a particular temperature called the Curie Point the values of the piezoelectric coefficients reach particularly high values. Above the Curie Point the crystal transformation is to a less polar form and the ferroelectric nature disappears. 

Copolymers of VF2 and trifluoroethylene also exhibit a Curie temperature at which the ferroelectric crystals show reversibly a solid state transformation to... 

Random copolymers of VF2/F3E when crystallized from the molten state above the Curie temperature show a microstructure in the form of very thin needle-like morphological units which are probably semicrystalline. Figure 5a illustrates the needle-like microstructure of the copolymer 80/20 melt crystallized in the paraelectric phase observed at 140 °C. After codling at room temperature the microstructure of the ferroelectric crystals is such that what appear in the optical microscope as radial fibers are, in fact, stacks of thin platelet-like morphological units (see Fig. 5b). 

Yamada et al. [9,10] demonstrated that the copolymers were ferroelectric over a wide range of molar composition and that, at room temperature, they could be poled with an electric field much more readily than the PVF2 homopolymer. The main points highlighting the ferroelectric character of these materials can be summarized as follows (a) At a certain temperature, that depends on the copolymer composition, they present a solid-solid crystal phase transition. The crystalline lattice spacings change steeply near the transition point, (b) The relationship between the electric susceptibility e and temperature fits well the Curie-Weiss equation, (c) The remanent polarization of the poled samples reduces to zero at the transition temperature (Curie temperature, Tc). (d) The volume fraction of ferroelectric crystals is directly proportional to the remanent polarization, (e) The critical behavior for the dielectric relaxation is observed at Tc. 

The crystals grown in this manner are in the form of clear sheets. The symmetry of the crystals is pseudotetragonal with a cell size of a0 = 3.841 A. and c0 = 32.83 A. Electrodes can be evaporated, or indium amalgam can be applied to the flat surfaces of the crystals, to produce samples for measurements. The d.c. resistance of the crystals is about 1012 fi-cm. They exhibit ferroelectric hysteresis loops up to the Curie temperature of 643°C. 

The origin of the pyroelectric effect, particularly in crystalline materials, is due to the relative motions of oppositely charged ions in the unit cell of the crystal as the temperature is varied. The phase transformation of the crystal from a ferroelectric state to a paraelectrlc state involves what is called a "soft phonon" mode (9 1). In effect, the excursions of the ions in the unit cell increase as the temperature of the material approaches the phase transition temperature or Curie temperature, T. The Curie temperature for the material used here, LiTaO, is 618 C (95). The properties of a large number of different pyroelectric materials is available through reference 87. For the types of studies envisaged here, it is preferable to use a pyroelectric material whose pyroelectric coefficient, p(T), is as weakly temperature dependent as possible. The reason for this is that if p(T) is independent of temperature, then the induced current in the associated electronic circuit will be independent of ambient temperature and will be a function only of the time rate of change of the pyroelectric element temperature. To see this, suppose p(T) is replaced by pQ. Then Equation U becomes... 

In comparison to ordinary dielectrics, the permittivities of the so-called ferroelectric materials are about 103 times larger. The ferroelectric material can be transformed into a new type of material called piezoelectric material by heating the ferroelectric above its Curie temperature and then cooling it in a powerful electric field. A piezoelectric crystal changes its polarization once subjected to a mechanical strain. As a result, it can deform mechanically under an electric field or produce electric impulses as a result of mechanical impulses. Currently, piezoelectric materials are widely used as force or pressure transducers with fast response times and very sensitive output. Permittivities of common dielectric and ferroelectric materials are given in Table 1.9. 

Of central importance for understanding the fundamental properties of ferroelec-trics is dynamics of the crystal lattice, which is closely related to the phenomenon of ferroelectricity [1]. The soft-mode theory of displacive ferroelectrics [65] has established the relationship between the polar optical vibrational modes and the spontaneous polarization. The lowest-frequency transverse optical phonon, called the soft mode, involves the same atomic displacements as those responsible for the appearance of spontaneous polarization, and the soft mode instability at Curie temperature causes the ferroelectric phase transition. The soft-mode behavior is also related to such properties of ferroelectric materials as high dielectric constant, large piezoelectric coefficients, and dielectric nonlinearity, which are extremely important for technological applications. The Lyddane-Sachs-Teller (LST) relation connects the macroscopic dielectric constants of a material with its microscopic properties - optical phonon frequencies ... 

Deuterium Isotope Effect. Ubbelohde and co-workers have done much work on the effect of deuterium substitution on the structures of H bonded crystals (1729, 2067, 1728, 1727, 2071, 522, 739, 2068). The results are reviewed in the summary paper, 2068. In most crystals the D bond is slightly longer than the H bond. Furthermore, in those crystals which are ferroelectric, the deuterated crystal has a higher ferroelectric transition temperature (upper Curie temperature). Some of the results summarized by Ubbelohde and Gallagher are... 

In some perovskite ceramics, the instability that occurs at the Curie temperature is not ferroelectric but rather antiferroelectric. In antiferroelectric crystals, the neighboring lines of ions are displaced in opposite senses which creates two alternating dipole sublattices of equivalent but opposite polarization. Consequently, the net polarization is zero, and the dielectric constant does change at the transition temperature. Examples of antiferroelectric crystals are WO3, NaNbO, PbZrO, and PbHfOj. 

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